Wavelet inverse transform method and apparatus and wavelet decoding method and apparatus

ABSTRACT

A wavelet inverse transform method includes a decoding object coefficient extracting step of extracting only coefficients necessary for decoding a specified area from wavelet transform coefficients, and a wavelet inverse transform step of inverse transforming coefficients extracted from the decoding object coefficient extracting step. The decoding object coefficient extracting step extracts transform coefficients not only inside the specified area but also those outside the specified area. This enables only an optional partial picture to be decoded without decoding the entire picture. A corresponding wavelet inverse transform device is also disclosed.

This application is a Continuation of U.S. application Ser. No.09/579,803, filed May 26, 2000, now U.S. Pat. No. 6,968,086, which ishereby incorporated by reference in its entirety herein.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a wavelet inverse transform method andapparatus used in extracting and decoding only transform coefficients ofa specified partial area from wavelet transform coefficients obtained onencoding by wavelet transform. This invention also relates to acorresponding wavelet decoding method and apparatus.

2. Description of Related Art

Among conventional typical picture compression systems, there is a JPEG(Joint Photographic Experts Group) system, standardized by the ISO(International Organization for Standardization). This system, employingan orthogonal transform, specifically the discrete cosine transform(DCT), is known to furnish a good encoded or decoded picture when ahigher number of allocated bits is used. However, if the number ofencoding bits is decreased to more than a certain extent, blockdistortion proper to DCT becomes outstanding so that subjectivedeterioration is apparent. On the other hand, such a system in which anentire picture is split into plural bands by a filter, termed a filterbank, comprising the combination of a high-pass filter and a low-passfilter, and encoding is performed from one band to another, is now beingresearched briskly. In particular, the wavelet encoding free from thedefect of block distortion, which becomes outstanding in highcompression such as is presented in DCT, is thought to be promising as atechnique which should take the place of the DCT.

Nowadays, an electronic still camera or a video movie exploits the JPEGor MPEG, with the transform system being the DCT. Since a product basedon the wavelet transform is predicted to be presented to the market intime to come, investigations in improving the efficiency in the encodingsystem are proceeding briskly in many research institutes. As a matterof fact, JPEG 2000, now being worked by ISO/IEC/JTC1_SC29/WG1, which isthe same organization as the JPEG, as a format the recommendation forthe standardization of which is scheduled to be issued in December 2000,is felt to be promising as the next-generation internationalstandardization system for still pictures. With this JPEG 2000, it hasalmost been established to use the wavelet transform in place of thepreexisting DCT of JPEG as a basic transformation system for picturecompression.

The present invention is directed to the elimination of the problem inexpanding only a partial area in wavelet inverse transform. That is, theentire wavelet transform coefficients are not read out and decoded, asis done in the conventional technique. This represents a significantmerit in reducing the memory capacity size. In the wavelet encoding,wavelet transform needs to be applied to the entire picture to store andhold the generated wavelet transform coefficients transiently in amemory. In wavelet decoding, the operation which is the reverse of thewavelet encoding operation is performed, thus necessitating an extremelylarge memory capacity for storing and holding the coefficients for theentire picture. Should the picture size be increased, the memorycapacity needs to be correspondingly increased. Thus, the conventionalpractice is not desirable for a device having a limited memory capacity,such as an electronic still camera, camcorder or PDA.

Recently, in e.g., the international standardization activities of JPEG2000, such a technique is investigated in which the entire picture of anobject of encoding is split into plural blocks to perform the encodingon the block basis. If the encoding by the encoder is done on the blockbases from the outset, partial decoding can be achieved by reading outan encoded bitstream associated with a pre-set block. However, therelacks up to now a research into partial decoding in the absence ofconstraint on the encoder.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide a waveletinverse transform method and apparatus and a wavelet decoding method andapparatus in which an encoded bitstream generated on wavelettransforming a usual entire picture is inputted to decode only anoptional partial picture without decoding the entire picture.

In one aspect, the present invention provides wavelet inverse transformdevice including decoding object coefficient extracting means forextracting only coefficients necessary for decoding a specified areafrom wavelet transform coefficients, and wavelet inverse transform meansfor inverse transforming coefficients extracted from the decoding objectcoefficient extracting means, wherein the decoding object coefficientextracting means extracts transform coefficients not only inside thespecified area but also those outside the specified area.

In another aspect, the present invention provides a wavelet inversetransform method including a decoding object coefficient extracting stepof extracting only coefficients necessary for decoding a specified areafrom wavelet transform coefficients, and a wavelet inverse transformstep of inverse transforming coefficients extracted from the decodingobject coefficient extracting means, wherein the decoding objectcoefficient extracting step extracts transform coefficients not onlyinside the specified area but also those outside the specified area.

In another aspect, the present invention provides a decoding deviceincluding entropy decoding means for entropy decoding an encodedbitstream, generated on wavelet inverse transforming a picture, decodingobject coefficient extracting means for extracting, from among wavelettransform coefficients obtained by the entropy decoding means, thosenecessary for decoding a specified area and wavelet inverse transformingmeans for inverse transforming the coefficients extracted by thedecoding object coefficient extracting means, wherein the decodingobject coefficient extracting means extracts transform coefficients notonly in the specified area but also those on an outer rim of thespecified area.

In another aspect, the present invention provides a wavelet decodingmethod including an entropy decoding step of entropy decoding an encodedbitstream, generated on wavelet inverse transforming a picture, adecoding object coefficient extracting step of extracting, from amongwavelet transform coefficients obtained by the entropy decoding step,those necessary for decoding a specified area and a wavelet inversetransforming step of inverse transforming the coefficients extracted bythe decoding object coefficient extracting step, wherein the decodingobject coefficient extracting step extracts transform coefficients notonly in the specified area but also those on an outer rim of thespecified area.

In the decoding object coefficient extracting means or step, wavelettransform coefficients required for decoding are extracted based on theinformation concerning an area determined by the decoding object areadetermining means or step determining the area of the decoding object.The transform coefficients, thus extracted, are inverse-transformed bythe wavelet inverse transform means or step. Of the transformcoefficients generated in the wavelet inverse transform means or step,those in a valid range are extracted based on overlap holdingprocessing.

The decoding object area determining means or step determines a decodingobject area by an external input or determining means or step to send aposition coordinate of apices in case of a rectangular area and theinformation on a center position as well as the radius in case of acircular area. The decoding object coefficient extracting means or stepextracts coefficients necessary for decoding the area in question tosend the extracted coefficients to the wavelet inverse transform meansor step. The decoding object coefficient extraction means or stepextracts coefficients necessary for decoding the area to send theextracted coefficients to the wavelet inverse transform means or step.The wavelet inverse transform means or step performs convolution byfilter coefficients having pre-set tap lengths and wavelet transformcoefficients to generate a decoded picture of the specified area.

According to the present invention, an encoded bitstream, generated onwavelet inverse transforming a usual entire picture, is inputted, todecode only an optional partial picture, without decoding the entirepicture.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a specified example of a wavelet inverse transform deviceaccording to the present invention and is a block diagram showing thestructure of a wavelet inverse transform device adapted for performingthe processing corresponding to the wavelet inverse transform methodaccording to the present invention.

FIG. 2 shows a decoding object area.

FIG. 3 is a block diagram showing the structure of an ordinary wavelettransform unit.

FIG. 4 shows band splitting of a two-dimensional picture.

FIG. 5 is a block diagram showing the structure of an ordinary waveletinverse transform unit.

FIG. 6 is a conceptual view showing wavelet coefficients on waveletsplitting up to two.

FIG. 7 shows an impulse response of a filter for performing wavelettransform.

FIG. 8 shows a decoding object range and a filtering range.

FIG. 9 shows partial decoding of a one-dimensional specified areaemploying an overlap holding method.

FIG. 10 shows partial decoding of a two-dimensional specified areaemploying an overlap holding method.

FIG. 11 shows a specified example of a wavelet decoding device accordingto the present invention and is a block diagram of a wavelet decodingdevice operating based on the wavelet decoding method of the presentinvention.

FIG. 12 is a block diagram showing the structure of a wavelet transformencoding device.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIGS. 1 to 10, a wavelet inverse transform device 10, as aspecified example of a wavelet inverse transform apparatus of thepresent invention, adapted for performing the processing correspondingto a wavelet inverse transform of the present invention, is explained indetail. Meanwhile, the wavelet inverse transform device 10 constitutes amain portion of a wavelet decoding device 60 which will be explainedsubsequently with reference to FIG. 11.

Among specified examples of application, there are an electronic camera,a portable telephone, a mobile picture transmission/reception terminal(PDA), a printer, an expander for a satellite image or an image formedical use, a software module thereof, an expander for a picture usedin a game or a three-dimensional CG, and a software module thereof.

Referring to FIG. 1, this wavelet inverse transform device 10 includes adecoding object area decision unit 11, a decoding object coefficientextraction unit 12 and a wavelet inverse transform unit 13.

The decoding object area decision unit 11 determines a decoding objectarea 11 by an external input or decision means provided in the decisionunit 11, to send out apex position coordinates if the decoding objectarea is a rectangular area, or to send out the center position and theradius information if the decoding object area is a circular area.

The decoding object coefficient extraction unit 12 extracts coefficientsrequired in decoding an area determined by the decoding object areadecision unit 11, from wavelet conversion coefficients 100 inputted froma coefficient input terminal 14, to send the extracted coefficients tothe wavelet inverse transform unit 13. In particular, this decodingobject coefficient extraction unit 12 extracts transform coefficientsnot only in a specified area but also transform coefficients lying on anouter rim of the specified area.

The wavelet inverse transform unit 13 inverse-transforms thecoefficients extracted by the decoding object coefficient extractionunit 12.

The operation of the above-described wavelet inverse transform device 10is hereinafter explained. First, the decoding object area decision unit11 determines an area in a picture to be decoded. For example, it isassumed that a partial areal picture at a center area (1, 1), from nineareas obtained on vertical 3 by horizontal 3 division, as shown in FIG.2, is to be decoded. For denoting the decoding object area, a numberdepicting the number of division in the vertical and horizontaldirections and the number of a block area as counted from a giventerminal side may be used. Alternatively, the upper left apex coordinateand the lower right apex coordinate of a shaded area may be used.

The decoding object area information 101, represented using any of theabove methods by the decoding object area decision unit 11, is enteredto the decoding object coefficient extraction unit 12 where waveletinverse transform coefficients 102 required for decoding are extracted.Such extraction of the wavelet transform coefficients will be discussedsubsequently in detail.

Here, the schematics of the wavelet transform and wavelet inversetransform, as basic techniques to which the present invention pertains,are explained.

FIG. 3 shows an ordinary structure of a wavelet transform unit. Thisunit performs octave splitting, as the most popular one of pluralwavelet transform technique, over plural levels. In the case of FIG. 3,the number of levels is three. Specifically, picture signals are splitinto a low range and a high range, with only the low range componentsbeing split hierarchically. Although FIG. 3 shows wavelet transform fora one-dimensional system, such as, for example, horizontal components ofa picture, for the sake of convenience, it may be extended to atwo-dimensional system in order to cope with the two-dimensionalsignals.

First, a picture photographed by a camera, not shown, is digitized toretrieve input picture signals 115 from an input terminal 20. Theseinput picture signals 115 are band-split by a low-pass filter 21 and ahigh-pass filter 22 to produce low range components and high rangecomponents which then are decimated by downsamplers 23, 23 in resolutionto one-half The operation up to this point is the level 1 which issuestwo outputs, namely an L (meaning low) output 116 and an H (meaninghigh) output 117. Only the low range component, obtained on decimation,are again band-split by a low-pass filter 24 and a high-pass filter 25and decimated in resolution by downsamplers 26, 26 to one-half. Theoperation up to this point is the level 2 which issues two outputs,namely an LL output 118 and an LH output 118. Only the low rangecomponent, that is the LL component 118, is again band-split by alow-pass filter 27 and a high-pass filter 28 and decimated in resolutionto one-half by downsamplers 29, 29. The operation up to this point isthe level 3. By performing the above-described processing up to apre-set level, the band components, obtained on hierarchicallyband-splitting the low range component, are generated sequentially. Theband components, generated at the level 3, are an LLL component 120 andan LLH component 121. The LLL component 120, LLH component 121, LHcomponent 119 and the H component 117 are outputted to outside at outputterminals 30, 31, 32 and 33, respectively.

FIG. 4 shows band components obtained on band splitting atwo-dimensional picture up to the level 2. It is noted that the notationof L and H in FIG. 4 differs from that of FIG. 3 dealing with theone-dimensional signal. That is, in FIG. 4, four components LL, LH, HLand HH are produced by level 1 band splitting in both the horizontal andvertical directions, where LL means that both the horizontal andvertical components are L and LH means that the horizontal component isH and the vertical component is L. The LL component is again band-splitto generate LLLL, LLHL, LLLH and LLHH.

The structure and the operation of the routine wavelet inverse transformis explained with reference to FIG. 5. When the band components,outputted by the wavelet transform explained in connection with FIG. 3,that is the LLL component 120, LLH component 121, LH component 119 andthe H component 117, are inputted at an input terminal 43, the LLLcomponent 120 and the LLH component 121 are first upsampled by a factorof two by upsamplers 44, 44. The low range component and the high rangecomponent are filtered in succession by a low-pass filter 49 and ahigh-pass filter 46, respectively, and synthesized together by an adder47. This completes the inverse transform of level 3, so that a bandcomponent LL118 is obtained. The band component LL118 and the LHcomponent 119 from the input terminal 42 are upsampled to a doubleresolution by upsamplers 48, 48. The low range component and the highrange component are filtered in succession by a low-pass filter 49 and ahigh-pass filter 50, respectively, and synthesized together by an adder51. This completes the inverse transform of level 2, so that a bandcomponent L116 is obtained. The band component L116 and the H component117 from the input terminal 43 are upsampled to a double resolution byupsamplers 52, 52. The low range component and the high range componentare filtered in succession by a low-pass filter 53 and a high-passfilter 54, respectively, and synthesized together by an adder 55. Thiscompletes the level 1 inverse transform so that an ultimateinverse-transformed decoded signal 115 is outputted at an outputterminal 56. The above is the basic structure and operation of theroutine wavelet inverse transform.

FIG. 6 represents the wavelet transform in connection the signal length.As a result of level 1 transform of the entire signal input x(n), twosorts of coefficients L and H, having a length equal to one-half that ofx(n), are generated. In addition, the level 2 transform splits the lowrange component L into coefficients LL and LH with one-half lengths.

In the present embodiment, a linear phase FIR filter is assumed, withthe tap length of filters used for wavelet transform and wavelet inversetransform being L, the number of impulse responses during the negativetime being Head and with the number of impulse responses during thepositive time excluding 0 being Tail. FIG. 7 shows a case wherein L=7,Head=3 and Tail=3. That is, according to the present invention, thetransform coefficients on the outer rim of a specified area areassociated with the number of impulses of the filter used for waveletinverse transform.

The filtering operation at the time of wavelet inverse transform isexplained with reference to FIG. 8 showing a case wherein a filter of anodd number tap length L=7 shown in FIG. 7 is used. It may be seen that,in filtering in both the horizontal and vertical directions, threecoefficients each on the left and right sides of the current position (dand k) are affected by filtering. Therefore, if the center position of acoefficient lies on the boundary of an area being inverse transformed,as in the case of the coefficients d and k, coefficients needs to beextracted from the neighboring area. In FIG. 8, now explained, thecoefficient area to be extracted in redundance are expressed as L_head,L_tail (low range), H_head, H_tail (high range).

FIG. 9 shows the distribution of band components when the wavelettransform is applied to a one-dimensional signal x(n) up to the level 2,it may be seen that a shaded portion 2 of x(n) is reflected by a portionindicated 2 in each of bands LL, LH and H. Therefore, in order tocalculate the wavelet transform coefficients of the level 1 from thelevel 2, the wavelet inverse transform means is in need of P2 partialcoefficients corresponding to the area 2, among the band components ofthe splitting level 2, partial coefficients in LL, along with L_head 2and L_tail 2, lying forwardly and backwardly thereof, and partialcoefficients in LH, along with H_head 2 and H_tail 2, lying forwardlyand backwardly thereof. 17.

Then, of the coefficients of the splitting level 1, obtained on inversetransform, as described above, only (L_head 1+2P2+L_tail) transformcoefficients, necessary by the overlap holding processing as laterexplained, are extracted. Then, P1 partial coefficients, lying in aportion 2 in the band H, are extracted, along with the coefficientsL_head and L_tail, lying ahead and at back of the P1 coefficients, areextracted. Then, from decoded signals, obtained on inverse transform ofextracted coefficients obtained on inverse transform of the level 2 LLand LH, and from the partial coefficients from H, the partial signalsx(2), corresponding to the target area 2, are taken out using overlapholding processing. The above is the explanation on the operation forthe one-dimensional system.

The overlap holding processing is introduced in, for example, NishiroTakaya, co-inventor of the present case, an assistant professor of TokyoMetropolitan University, “Fast Fourier Transform and its Application”,published by SHOKODO, pp. 109 to 112. This technique is a method oflinear convolution of an infinite input sequence and features employingoverlapping data in dividing input data into blocks and also employingcyclic convolution as the block-based convolution. In the cyclicconvolution, initial overlapping portions of the cyclic convolution aretruncated. There is no necessity of summing the results of the cyclicconvolution.

The two-dimensional wavelet inverse transform is now explained withreference to FIG. 10, showing areas of wavelet transform coefficients,required from one splitting level to another, when the shaded portion inFIG. 2 is to be decoded, such areas being shown shaded in FIG. 10.

For completely decoding the target partial picture, it is necessary toextract and inverse-transform surrounding coefficients, shown by brokenlines in FIG. 10, as discussed above. Since FIG. 10 shows a case whereinthe dividing level is three, the inverse transform is performed usingpartial coefficients of the extracted four areas in performing the level3 decoding. From the next level on, decoding is performed using thethree partial coefficients of the level in question and the completelydecoded results of the previous level. This sequence of operations isrepeated to realize the partial decoding.

In FIG. 10, Pheadi and Ptaili denote the number of coefficients requiredto be added on the left and upper sides at level i and that required tobe added on the right and lower sides at level i, respectively. Thesecoefficients are extracted from the outer rim side of the object area,as discussed above. In the two-dimensional system, only validcoefficients at each inverse transform level are selected and extractedby the overlap holding processing. The foregoing is the explanation onthe partial decoding of a two-dimensional picture.

A wavelet decoding device 60, as a specified example of the waveletdecoding device of the present invention, operating by the waveletdecoding method of the present invention, is now explained withreference to FIG. 11. This wavelet decoding device 60 represents aspecified example of the wavelet inverse transform device 10 built intoa decoding device.

This wavelet decoding device 60 includes an entropy decoding unit 62, adequantizer 63, a transform coefficient back-scanning unit 64 and theabove-mentioned wavelet inverse transform device 10.

The entropy decoding unit 62 entropy-decodes an encoded bitstreamgenerated on wavelet transform encoding a picture.

When the wavelet transform coefficients are being quantized in thewavelet transform encoding, the dequantizer 63 dequantizes thequantization coefficients obtained at the entropy decoding unit 62 torestore the dequantized quantization coefficients to 26.

If the transform coefficients are being scanned to raise the encodingefficiency in the wavelet transform encoding, the transform coefficientback-scanning unit 64 back-scans the transform coefficients to restorethe original coefficients. It is wavelet transform coefficients 107 fromthis transform coefficient back-scanning unit 64 that are routed to thedecoding object coefficient extraction unit 12 of the wavelet inversetransform device 10.

Before proceeding to description of the wavelet decoding device 60,reference is had to FIG. 12 to explain an associated wavelet transformencoding device 70.

The wavelet transform encoding device 70 is made up of a wavelettransform unit 72, a transform coefficient scanning unit 73, a quantizer74 and an entropy encoding unit 75.

First, a picture photographed by a camera, not shown, is digitized andinput picture signals 110 are retrieved at an input terminal 71. Thewavelet transform unit 72 generates transform coefficients 111 from theinput picture signals 110 to send the generated transform coefficients111 to the transform coefficient scanning unit 73, which then scans thetransform coefficients to re-array the coefficients such as to improvethe encoding efficiency. For example, it is assumed here that thewavelet transform coefficients are scanned from left to right (in thehorizontal direction) and from above to below (in the verticaldirection). The as-scanned coefficients 112, obtained on re-arraying inthe transform coefficient scanning unit 73, are quantized by thequantizer 74 from which quantized coefficients 113 are outputted to theentropy encoding unit 75.

It suffices for the quantizer 74 to employ routinely used scalarquantization as indicated by the following equation:Q=x/Δ  (1)where x is a value of the wavelet transform coefficient and Δ is aquantization index value.

The entropy encoding unit 75 applies information source encoding to thequantized coefficients 113 by way of information compression. As theinformation source encoding at this entropy encoding unit 75, theHuffman encoding or the arithmetic encoding may be used. An ultimateencoded bitstream 114 is sent out via the entropy encoding unit 75 to anoutput terminal 76.

The operation of the wavelet decoding device 60 is hereinafterexplained. An encoded bitstream 104 is sent via an input terminal 61 tothe entropy decoding unit 62, which then entropy-decodes the encodedbitstream 104 to send the resulting quantized coefficients 105 to thedequantizer 63.

The dequantizer 63 dequantizes the quantized coefficients 105 to outputthe dequantized transform coefficients. Meanwhile, the entropy decodingunit 62 needs to be a counterpart device of the entropy encoding unit75.

It suffices for the dequantizer 63 to employ routinely used scalardequantization as indicated by the following equation:x=Qx/Δ  (2)where Q is a value of the quantization coefficient and Δ is aquantization index value.

The transform coefficients 106 are sent to the transform coefficientback-scanning unit 64 which then applies back-scanning transform, as areverse procedure to the operation performed by the transformcoefficient scanning unit 73, to the transform coefficients 106 togenerate the original transform coefficients. The resulting transformcoefficients 107 are inputted to the decoding object coefficientextraction unit 12 of the wavelet inverse transform device 10. Theensuing operation is the same as that described above and hence is notexplained for simplicity.

In the wavelet decoding device 60, shown in FIG. 11, it is possible todecode only a desired portion of a picture, without it being necessaryto input an encoded bitstream produced on wavelet transform of an entirepicture to decode the entire picture, as is done in the conventionalpractice. Of course, there is imposed no constraint on the encodingdevice 70 to split the picture into plural areas at the outset toperforming the encoding.

The fact that only an optional portion needs to be decoded gives threefavorable results, that is the results that the processing volume ofconvolution in filtering may be reduced, the memory width may also bereduced and that the memory accessing frequency can be diminished.

There is also such merit that, by exploiting overlap holding processing,the operation on the encoder side may be the reverse of that on thedecoder side and vice versa so that the teaching of the presentinvention can be applied to lossless encoding.

Moreover, since it suffices to read out transform coefficients of andecoding object, there is no necessity of limiting the partial area ofthe decoding object to a rectangular area such that an area of a circleor a more complex figure can be dealt with.

Although the configuration of the present invention has been stated tobe implemented by hardware, it may, of course, be implemented bysoftware.

1. A wavelet transform device comprising: decoding object coefficient extracting means for extracting, from a plurality of wavelet transform coefficients, partial coefficients necessary for decoding a specified area of a picture; and wavelet inverse transform means for inverse transforming said extracted partial coefficients, wherein said extracted partial coefficients are wavelet transform coefficients that include said specified area of every split level and outside said specified area, wherein said wavelet inverse transform means transforms using the three partial coefficients of the level and the completely transformed results of the previous level when one or more levels other than a max level are transformed.
 2. The wavelet inverse transform device according to claim 1 further comprising: decoding object area determining means for determining a decoding object area, said decoding object coefficient extracting means extracting coefficients necessary for decoding an area determined by said decoding object area determining means.
 3. The wavelet inverse transform device according to claim 1 wherein said wavelet transform coefficients are made up of transform coefficients of a plurality of splitting levels and include transform coefficients inside of and on an outer rim side of each splitting level based specified area.
 4. The wavelet inverse transform device according to claim 1 wherein transform coefficients on the outer rim side of the specified area extracted by said decoding object coefficient extracting means correspond to the number of impulse response of a filter used in said wavelet inverse transform means.
 5. The wavelet inverse transform device according to claim 3 wherein said wavelet transform coefficients are obtained on hierarchically splitting a low range component of a plurality of splitting levels.
 6. The wavelet inverse transform device according to claim 1 wherein, of transform coefficients generated by said wavelet inverse transform means, those in a valid range based on overlap holding processing are extracted.
 7. The wavelet inverse transform device according to claim 6 wherein extraction of the coefficients in the valid range based on said overlap holding processing is performed from one level of the wavelet splitting to another.
 8. A wavelet inverse transform method comprising: decoding object coefficient extracting step for extracting, from a plurality of wavelet transform coefficients, partial coefficients necessary for decoding a specified area of a picture; and wavelet inverse transform step for inverse transforming said extracted partial coefficients, wherein said extracted partial coefficients are wavelet transform coefficients that include said specified area of every split level and outside said specified area, said wavelet inverse transform transforms step using the three partial coefficients of the level and the completely transformed results of the previous level when one or more levels other than a max level are transformed.
 9. The wavelet inverse transform method according to claim 8, wherein decoding object coefficient extracting step extracts transform coefficients outside said specified area that are necessary for decoding at least one of said transform coefficients inside said specified area.
 10. A wavelet decoding device comprising: entropy decoding means for entropy decoding an encoded bitstream, generated on wavelet inverse transforming a picture; decoding object coefficient extracting means for extracting, from a plurality of wavelet transform coefficients obtained by said entropy decoding means, partial coefficients necessary for decoding a specified area of said picture; and wavelet inverse transform means for inverse transforming said extracted partial coefficients of said specified area, wherein said extracted partial coefficients are wavelet transform coefficients that include said specified area of every split level and outside said specified area, said wavelet inverse transform means transforms using the three partial coefficients of the level and the completely transformed results of the previous level when one or more levels other than a max level are transformed.
 11. The wavelet decoding device according to claim 10 further comprising: dequantizing means to restore wavelet transform coefficients obtained by said entropy decoding means to restore wavelet transform coefficients, said decoding object coefficient extracting means for extracting coefficients necessary for decoding the specified area from among the wavelet transform coefficients obtained by said dequantizing means.
 12. The wavelet inverse transform device according to claim 10 wherein decoding object area determining means for determining a decoding object area, said decoding object coefficient extracting means extracting coefficients necessary for decoding an area determined by said decoding object area determining means.
 13. The wavelet inverse transform device according to claim 10 wherein said wavelet transform coefficients are made up of transform coefficients of a plurality of splitting levels and include transform coefficients inside of and on an outer rim side of each splitting level based specified area.
 14. The wavelet inverse transform device according to claim 10 wherein transform coefficients on the outer rim side of the specified area extracted by said decoding object coefficient extracting means correspond to the number of impulse responses of a filter used in said wavelet inverse transform means.
 15. The wavelet inverse transform device according to claim 12 wherein said wavelet transform coefficients are obtained on hierarchically splitting a low range component of a plurality of splitting levels.
 16. The wavelet inverse transform device according to claim 10 wherein, of transform coefficients generated by said wavelet inverse transform means, those in a valid range based on overlap holding processing are extracted.
 17. The wavelet inverse transform device according to claim 15 wherein extraction of the coefficients in the valid range based on said overlap holding processing is performed from one level of the wavelet splitting to another.
 18. A wavelet decoding method comprising: entropy decoding step for entropy decoding an encoded bitstream, generated on wavelet inverse transforming a picture; decoding object coefficient extracting step for extracting, from a plurality of wavelet transform coefficients obtained by said entropy decoding step, partial coefficients necessary for decoding a specified area of said picture; and wavelet inverse transform step for inverse transforming said extracted partial coefficients of said specified area, wherein said extracted partial coefficients are wavelet transform coefficients that include said specified area of every split level and outside said specified area, said wavelet inverse transform step transforms using the three partial coefficients of the level and the completely transformed results of the previous level when one or more levels other than a max level are transformed.
 19. The wavelet decoding method according to claim 18 further comprising: dequantizing step to restore wavelet transform coefficients obtained by said entropy decoding means to restore wavelet transform coefficients, said decoding object coefficient extracting step for extracting coefficients necessary for decoding the specified area from among the wavelet transform coefficients obtained by said dequantizing step.
 20. The wavelet decoding method according to claim 18, wherein decoding object coefficient extracting step extracts transform coefficients outside said specified area that are necessary for decoding at least one of said transform coefficients inside said specified area. 